Question

Aflati numerele naturale x,y,z daca:

a) 17 supra 2x - 1 este supraunitara
b) y supra 27 = 8 supra 12
c) z + 2 supra 2z - 1 = 2 supra 3

Dau coroana

Answer 1

a)
$\frac{17}{2x - 1} \: supraunitara \: \\ 2x - 1 > 17 \\ 2x > 18$
x={10,11,12,13,....}
b)
$\frac{y}{27} = \frac{8}{12} \\ y = \frac{27 \times 8}{12} = 18$
c)
$\frac{z + 2}{2z - 1} = \frac{2}{3} \\ (z + 2) \times 3 = (2z - 1) \times 2 \\ 3z + 6 = 4z - 2 \\ 6 + 2 = z \\ \: z = 8$